(-3,0), (0,-4), (2,0), (2,5). This is not a function of X. But what's the best explanation for why out of these choices.
a
(-3, 0) has a negative x-value.
b
(2, 0) and (2, 5) have the same x-value but different y-values.
c
(0, -4) has a negative y-value.
d
(-3, 0) and (2, 0) have the same y-value but different x-values.

B

Step-by-step explanation:

Let's eliminate our options

A: The answer is not A because functions can have negative x values.

B: This one immediately seems right to me because a function cannot have one input that spits out two outputs. This would fail the vertical line test

C: Like A, having negative values in either the x position or y position does not rule out a function. e.g. y = x - 4

D: Unlike B, having two of the same y coordinates does not rule out a function. The function could be quadratic. e.g. y = (x+3)(x-2)

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4